At energies much smaller than the Planck Mass \(M_P^2=G^{-1}\) , with \(G\)  the Newton constant, one can write down a generic action for gravitational interactions organized as a tower of operators with an increasing number of derivatives [1]}, [2]}


Sgrav=d4 x-g{22R+c1 R2+c2 RR+c3 RR
+...} ,

where \(\kappa ^2=32\pi G\) , \(R_{\mu \nu \alpha \beta }\)  is the curvature tensor, \(R_{\mu \nu }\)  the Ricci tensor and \(R\)  the curvature. A derivative counts as \({\cal O}(p)\) , with \(p\)  a typical external momentum so that each \(R,\, R_{\mu \nu },\, R_{\mu \nu \alpha \beta } \sim p^2\) . In addition, every graviton takes a factor \(G^{1/2}\)  because of the typical splitting of the total metric \(g_{\mu \nu }=\eta _{\mu \nu }+\kappa h_{\mu \nu }\) , with \(\eta _{\mu \nu }\)  the Minkowski metric and \(h_{\mu \nu }\)  the perturbation linear in the graviton field. In the case of pure gravity the counterterms \(c_i=0\) , \(i=1,2,3\) , and corrections are \({\cal O}(p^3)\)  and higher [3]}. Then, for energies \(E\ll \Lambda \)  with \(\Lambda \sim G^{-1/2}\approx 10^{19}\)  GeV, gravity can be seen as a low-energy Effective Field Theory (EFT). Here we have identified the cutoff of the theory with the so-called unitary cutoff \(\Lambda _U\)  of the gravity low-energy EFT [4]}, [5]}, [6]}.
